Program crashes after checking index at array - c++

Question

Please note: I am not sure if this fits here, if not, please move to the proper forum.
So I have a progrmam that tries to solve th Traveling Salesman Problem, TSP for short.
My code seems to run fine until I try to use 33810 cities, in which the program crashes after trying to access the position costs[69378120], it simply stops responding and end soon after.
I am trying the folowing code:
#include <iostream>
#include <stdlib.h>
#include <malloc.h>
#include <fstream>
#include <math.h>
#include <vector>
#include <limits>
using namespace std;
typedef long long int itype;
int main(int argc, char *argv[]) {
itype n;
ifstream fenter;
fenter.open(argv[1]);
ofstream fexit;
fexit.open(argv[2]);
fenter>> n;
double *x;
double *y;
x = (double*) malloc(sizeof(double)*n);
y = (double*) malloc(sizeof(double)*n);
cout<<"N : "<<n<<endl;
for (int p = 0; p < n; p++) {
fenter>> x[p] >> y[p];
}
fenter.close();
int *costs;
costs = (int*) malloc(sizeof(int)*(n*n));
for (int u = 0; u < n; u++) {
for (int v = u+1; v < n; v++) {
itype cost = floor(sqrt(pow(x[u] - x[v], 2) + pow(y[u] - y[v], 2)));
cout<<"U: "<<u<<" V: "<<v<<" COST: "<<cost<<endl;
costs[u*n + v] = cost;
cout<<"POS (u*n + v): "<<(u*n + v)<<endl;
cout<<"POS (v*n + u): "<<(v*n + u)<<endl;
costs[v*n + u] = cost;
}
}
return 0;
}
According with some verifications, the cost array should use 9.14493GB, but Windows only gives 0.277497GB. Then after triying to read costs[69378120], it closes.
For now, I not worried about the efficiency, nor the solution to the TSP, just need to fix this issue. Any clues?
---UPDATE---
Following the sugestions I tried changing a few things. the result is the code below
int main(int argc, char *argv[]) {
int n;
ifstream entrada;
entrada.open(argv[1]);
ofstream saida;
saida.open(argv[2]);
entrada >> n;
vector<double> x(n);
vector<double> y(n);
for (int p = 0; p < n; p++) {
entrada >> x[p] >> y[p];
}
entrada.close();
vector<itype> costs(n*n);
if(costs == NULL){ cout << "Sem memória!" << endl; return -1;}
for (int u = 0; u < n; u++) {
for (int v = u+1; v < n; v++) {
itype cost = floor(sqrt(pow(x[u] - x[v], 2) + pow(y[u] - y[v], 2)));
costs[u*n + v] = cost;
costs[v*n + u] = cost;
}
}
return 0;
}
The problem still persists

Answer 1

If compiling in 32-bit size_t is 32 bit and then
1143116100*4
is larger than the largest 32-bit number hence int overrun.
Compiling in 64-bit
size_t siz = 1143116100;
std::vector<long long> big(siz);
std::cout << big.size() << ", " << big.max_size() << std::endl;
which prints
1143116100, 2305843009213693951
if I change it to
size_t siz = 1024*1143116100;
I get a bad_alloc as my swap disk is not big enough for that.